Geodesic
Support functions of convex compacta
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 203-213.

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The properties of the space $\mathscr L(X'_\varkappa)$ of all sublinear functionals, defined on a space $X'$ (topologically adjoint to a Hausdorff locally convex barrelled space $X$) and continuous in the Arens topology $\varkappa(X',X)$, equipped with topology of uniform convergence on bounded subsets of $X$prime are studied. It is shown that completeness and separability of a space $X$ are hereditary for $\mathscr L(X'_\varkappa)$. Criteria for the compactness of subsets of $\mathscr L(X'_\varkappa)$ and conditions for the metrizability of compacta in $\mathscr L(X'_\varkappa)$ are given. The topological isomorphism between $\mathscr L(X'_\varkappa)$ and the space of all nonempty convex compacta in $X$ with the Vietoris topology is established. The results obtained here are applied for the study of the properties of multiple-valued integrals. 
@article{MZM_1977_22_2_a4,
     author = {A. A. Tolstonogov},
     title = {Support functions of convex compacta},
     journal = {Matemati\v{c}eskie zametki},
     pages = {203--213},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a4/}
}
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A. A. Tolstonogov. Support functions of convex compacta. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 203-213. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a4/